How many of g of S are required to produce 30 moles and 20 g of `H_(2)SO_(4)` respectively?

Options

A. 450g, 2.45g
B. 960g,6.53g
C. 104g,2.23g
D. None of these

Explanation

To determine how many grams of sulfur (S) are required to produce 30 moles and 20 grams of sulfuric acid (H₂SO₄), we can follow these steps:

### Step 1: Calculate grams of sulfur needed for 30 moles of H₂SO₄

1. **Find the molar mass of H₂SO₄**:
- The molar mass of H₂SO₄ is calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol × 1 = 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol
- Total molar mass of H₂SO₄ = 2 + 32 + 64 = 98 g/mol

2. **Determine the amount of sulfur in 30 moles of H₂SO₄**:
- In 1 mole of H₂SO₄, there is 1 mole of sulfur, which is 32 grams.
- Therefore, in 30 moles of H₂SO₄:
\[ \text{Grams of S} = 30 \text{ moles} \times 32 \text{ g/mole} = 960 \text{ g} \]

### Step 2: Calculate grams of sulfur needed for 20 grams of H₂SO₄

1. **Determine the fraction of sulfur in 20 grams of H₂SO₄**:
- We already know that 98 grams of H₂SO₄ contains 32 grams of sulfur.
- To find how much sulfur is in 20 grams of H₂SO₄:
\[ \text{Grams of S} = \left(\frac{32 \text{ g}}{98 \text{ g}}\right) \times 20 \text{ g} \]
- Calculate:
\[ \text{Grams of S} = \frac{32 \times 20}{98} \approx 6.53 \text{ g} \]

### Final Answers:
- For 30 moles of H₂SO₄: 960 g of sulfur are required.
- For 20 g of H₂SO₄: approximately 6.53 g of sulfur are required.